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2018 Numerical Procedures for Random Differential Equations
Mohamed Ben Said, Lahcen Azrar, Driss Sarsri
J. Appl. Math. 2018: 1-23 (2018). DOI: 10.1155/2018/7403745


Some methodological approaches based on generalized polynomial chaos for linear differential equations with random parameters following various types of distribution laws are proposed. Mainly, an internal random coefficients method ‘IRCM’ is elaborated for a large number of random parameters. A procedure to build a new polynomial chaos basis and a connection between the one-dimensional and multidimensional polynomials are developed. This allows handling easily random parameters with various laws. A compact matrix formulation is given and the required matrices and scalar products are explicitly presented. For random excitations with an arbitrary number of uncertain variables, the IRCM is couplet to the superposition method leading to successive random differential equations with the same main random operator and right-hand sides depending only on one random parameter. This methodological approach leads to equations with a reduced number of random variables and thus to a large reduction of CPU time and memory required for the numerical solution. The conditional expectation method is also elaborated for reference solutions as well as the Monte-Carlo procedure. The applicability and effectiveness of the developed methods are demonstrated by some numerical examples.


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Mohamed Ben Said. Lahcen Azrar. Driss Sarsri. "Numerical Procedures for Random Differential Equations." J. Appl. Math. 2018 1 - 23, 2018.


Received: 2 February 2018; Accepted: 26 March 2018; Published: 2018
First available in Project Euclid: 13 June 2018

zbMATH: 07132105
MathSciNet: MR3809499
Digital Object Identifier: 10.1155/2018/7403745

Rights: Copyright © 2018 Hindawi


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